It looks like you've uploaded a worksheet titled
"Area of a Rhombus" with several problems asking to find the area of each rhombus. The formula for the area of a rhombus is:
$$
A = \frac{1}{2} \times d_1 \times d_2
$$
where $d_1$ and $d_2$ are the lengths of the diagonals.
Alternatively, if side length and height are given, you can use:
$$
A = \text{base} \times \text{height}
$$
But in most cases on this worksheet, the diagonals are shown or implied.
Let’s go through each problem one by one and solve them step-by-step.
---
Problem 1
Given:
- Diagonals: 6 yd and 8 yd
Step 1: Use the formula:
$$
A = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 6 \times 8
$$
Step 2: Calculate:
$$
A = \frac{1}{2} \times 48 = 24
$$
Answer: $ A = 24 \text{ yd}^2 $
---
Problem 2
Given:
- Diagonals: 10 ft and 11 ft
Step 1: Apply the formula:
$$
A = \frac{1}{2} \times 10 \times 11
$$
Step 2: Calculate:
$$
A = \frac{1}{2} \times 110 = 55
$$
Answer: $ A = 55 \text{ ft}^2 $
---
Problem 3
Given:
- Diagonals: 7 in and 10 in
Step 1: Use the formula:
$$
A = \frac{1}{2} \times 7 \times 10
$$
Step 2: Calculate:
$$
A = \frac{1}{2} \times 70 = 35
$$
Answer: $ A = 35 \text{ in}^2 $
---
Problem 4
Given:
- Diagonals: 12 ft and 10 ft (from the image)
Wait — let's double-check: the figure shows two diagonals intersecting at right angles. One diagonal is labeled 12 ft, and the other appears to be split into two 5 ft segments → so total length = 10 ft.
So:
- $d_1 = 12$, $d_2 = 10$
Step 1:
$$
A = \frac{1}{2} \times 12 \times 10 = \frac{1}{2} \times 120 = 60
$$
Answer: $ A = 60 \text{ ft}^2 $
---
Problem 5
Given:
- Diagonals: 24 cm and 18 cm (based on typical labeling — one diagonal is 24 cm, the other is split into 9 cm and 9 cm → total 18 cm)
Step 1:
$$
A = \frac{1}{2} \times 24 \times 18
$$
Step 2:
$$
= \frac{1}{2} \times 432 = 216
$$
Answer: $ A = 216 \text{ cm}^2 $
---
✔ Final Answers:
| Problem | Area |
|--------|------|
| 1 | 24 yd² |
| 2 | 55 ft² |
| 3 | 35 in² |
| 4 | 60 ft² |
| 5 | 216 cm² |
---
🔍 Explanation:
The key idea is that
the diagonals of a rhombus bisect each other at right angles, forming four right triangles. The area of a rhombus can be found using the formula:
$$
\text{Area} = \frac{1}{2} \times d_1 \times d_2
$$
This is because the rhombus can be divided into two congruent triangles along one diagonal, and then further into four right triangles. The total area becomes half the product of the diagonals.
You can also verify by multiplying the full lengths of the diagonals and dividing by 2.
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If you'd like me to help fill out the worksheet with all steps written in the "WORK AREA" section, I can format it exactly as it should appear! Just let me know.
Parent Tip: Review the logic above to help your child master the concept of area of rhombus worksheet.
